Details

sample28.0ms

Algorithm

intervals

Results

10.0ms	69×	body	1280	valid
6.0ms	61×	body	640	valid
3.0ms	161×	body	80	valid
2.0ms	25×	body	320	valid
1.0ms	12×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	3
1	13	3
2	15	3
3	15	3

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 40.6b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
4.4b	(- (exp x) 1.0)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `associate-/r*`
2×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 68

Calls

2 calls:

7.0ms	(/ (- (exp x) 1.0) x)
5.0ms	(- (exp x) 1.0)

series61.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(/ (- (exp x) 1.0) x)
16.0ms	(- (exp x) 1.0)

simplify36.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	282	468
1	919	380
2	5001	377

prune122.0ms

Filtered

74 candidates to 52 candidates (70.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	71	3	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	3	75

Merged error: 0.1b

Counts

75 → 3

localize7.0ms

Local error

Found 1 expressions with local error:

0.1b	(fma 1/6 (pow x 2) (fma 1/2 x 1))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma 1/6 (pow x 2) (fma 1/2 x 1))

series21.0ms

Counts

1 → 3

Calls

1 calls:

21.0ms

(fma 1/6 (pow x 2) (fma 1/2 x 1))

simplify25.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	36	59
1	104	52
2	535	52
3	5002	52

prune30.0ms

Filtered

13 candidates to 10 candidates (76.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	13	0	13
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	13	3	16

Merged error: 0.1b

Counts

16 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) 1.0)
0.0b	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
0.0b	(/ (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)) x)
4.6b	(fma (- 1.0) 1.0 (exp (+ x x)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
99×	`*-un-lft-identity`
65×	`add-sqr-sqrt` `add-cube-cbrt`
21×	`associate-/l*`
17×	`distribute-lft-out`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
7×	`associate-/r*`
6×	`flip3-+` `flip-+` `div-inv` `add-log-exp`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`fma-def`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `sum-log` `fma-udef` `associate-/l/`

Counts

4 → 154

Calls

4 calls:

4.0ms	(+ (exp x) 1.0)
6.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
10.0ms	(/ (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)) x)
1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))

series227.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (exp x) 1.0)
63.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
109.0ms	(/ (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)) x)
41.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))

simplify64.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	531	2009
1	1917	1909
2	5001	1904

prune377.0ms

Filtered

166 candidates to 127 candidates (76.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	162	4	166
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	163	6	169

Merged error: 0.1b

Counts

169 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
4.6b	(fma (- 1.0) 1.0 (exp (+ x x)))
4.6b	(fma (- 1.0) 1.0 (exp (+ x x)))
4.6b	(fma (- 1.0) 1.0 (exp (+ x x)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-prod` `*-un-lft-identity`
12×	`add-sqr-sqrt` `add-cube-cbrt` `times-frac`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef` `distribute-lft-out`
2×	`associate-/r/`
1×	`cbrt-div` `flip3-+` `pow1/3` `flip-+` `div-inv`

Counts

4 → 59

Calls

4 calls:

6.0ms	(cbrt (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))

series321.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(cbrt (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
47.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
41.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
46.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))

simplify69.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (61.0ms)

Iter	Nodes	Cost
0	227	703
1	585	654
2	2358	637
3	5002	628

prune223.0ms

Filtered

71 candidates to 61 candidates (85.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	71	6	77

Merged error: 0.1b

Counts

77 → 6

regimes69.0ms

Accuracy

98.6% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 20.9b

bsearch37.0ms

Steps

Iters	Range		Point
8	-0.002595282603730271	-2.587228857819641e-07	-0.00014843984217390087

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	53
1	37	53

end0.0ms

sample863.0ms

Algorithm

intervals

Results

389.0ms	2326×	body	1280	valid
172.0ms	1649×	body	640	valid
98.0ms	5399×	body	80	valid
55.0ms	836×	body	320	valid
18.0ms	423×	body	160	valid